Quantum communication on the bosonic loss-dephasing channel

Quantum optical systems are typically affected by two types of noise: photon loss and dephasing. Despite extensive research on each noise process individually, a comprehensive understanding of their combined effect is still lacking. A crucial problem lies in determining the values of loss and dephasing for which the resulting loss-dephasing channel is antidegradable, implying the absence of codes capable of correcting its effect or, alternatively, capable of enabling quantum communication. A conjecture [Quantum 6, 821 (2022)2521-327X10.22331/q-2022-09-29-821] suggested that the bosonic loss-dephasing channel is not antidegradable if the loss is below 50%. In this paper we refute this conjecture, specifically proving that for any value of the loss, if the dephasing is above a critical value, then the bosonic loss-dephasing channel is antidegradable. While our result identifies a large parameter region where quantum communication is not possible, we also prove that if two-way classical communication is available, then quantum communication - and thus quantum key distribution - is always achievable, even for high values of loss and dephasing.